Online Millimeter Wave Phased Array CalibrationBased on Channel Estimation

Thomas Moon, Junfeng Gaun, Haitham HassaniehElectrical and Computer Engineering, University of Illinois at Urbana-Champaign, USA

Abstract—This paper proposes a new over-the-air (OTA) cali-bration method for millimeter wave phased arrays. Our methodleverages the channel estimation process which is a fundamentalpart of any wireless communication system. By performing thechannel estimation while changing the phase of an antennaelement, the phase response of the element can be estimated.The relative phase of the phased array can also be obtainedby collecting all the estimated phase responses with a sharedreference state. Hence, the phase mismatches of the phased arraycan be resolved. Unlike prior work, our calibration methodembraces all the array components such as power-divider, phaseshifter, amplifier and antenna and thus, spans the full chain. Byoverriding channel estimation, our proposed technique does notrequire any additional circuits for calibration. Furthermore, thecalibration can be performed online without the need to pausethe communication. We tested our method on an eight elementphased array at 24GHz which we designed and fabricated in PCBfor verification. The measured beam pattens prove the viabilityof our proposed method.

Index Terms—Phased Array, Millimeter Wave, Calibration,Beamforming, Over-the-air measurement

I. INTRODUCTION

The surge of IoT and mobile devices has led to an explosiveincrease in demand for wireless bandwidth. This promptedthe FCC to open multi-GHz of both license and unlicensedspectrum in the millimeter wave (mmWave) frequency bandsabove 24 GHz [1]. Millimeter wave is expected to deliverwireless link at fiber-like speeds of multi-Gbps and will play acentral role in 5G cellular networks and future wireless LANs.However, mmWave signals attenuate quickly with distance.Hence, mmWave radios need to use directional antennas tofocus the signal power and extend the range.

The key enabler for directionality in mmWave are phasedarrays. The small wavelength of mmWave frequencies allow usto pack a very large number of antennas in a small area whichcreates highly directional narrow beams. Phased arrays allowus to electronically steer the direction of the beam in real-time in order to accommodate mobility and adapt to dynamicenvironments. A phased array works by changing the phase ofthe signal on each antenna element using a phase shifter. Thephase shifter values are chosen in order to align the phase ofthe signals in a given direction θ to sum up constructively andbeamform the signal towards θ.

However, due to the very small wavelength, mmWavephased arrays are extremely sensitive to small offsets in thedesign of the array and the output of the phase shifters. Specif-ically, process variation and RMS phase error of the phaseshifters typically become significant at mmWave frequency

(a) Before Calibration (b) After Calibration

Fig. 1. Phased array beam pattern when directed towards 100◦ (a) beforeand (b) after calibration. .

because the device feature size scales down [2]–[4]. Nanoscaletransistors at mmWave frequency are more susceptible tolong-term electrical stress. Even a single transistor aging candegrade circuit performance [5], [6]. Furthermore, temperaturedrifts also produce large degradation on the performanceof phase shifting [7]. Without calibrating for these offsetsand errors, the array can end up beamforming the signalin many directions which limits the gain of the array andthe performance of the mmWave system while at the sametime creating interference in other directions. Fig. 1 shows anexample of the beam pattern of an 8 element phased arrayoperating at 24 GHz before and after calibration. As can beseen, without calibration, the beam is not directional. It hasmore than one main lobe and a significant number of sidelobes.

Unfortunately, calibrating the phased array requires expen-sive equipment like vector network analyzers (VNAs) whichcan cost more than half a million dollars at mmWave frequen-cies [8] and cannot be used to calibrate mass production ofmmWave phased arrays or recalibrate the arrays after beingused. To reduce calibration cost and reliance on external testequipment, built-in self test (BIST) has been proposed as analternative solution for phased array testing [9]–[13]. In [9],[10], [14], on-chip BIST circuitry is demonstrated: it is ableto characterize and calibrate the amplitude and phase of eachchannel of the phased array. The BIST technique can generallyachieve accurate measurements on the target system due toits proximity. To further reduce the test time on large scalephased arrays, parallel and tuning algorithms are presented in[12], [13]. The approach in [12] applies code-modulation toeach element in the array to allow parallel measurements usingBIST architecture on the distribution network. Concurrenttesting on all mixed/RF components in MIMO is demonstratedusing multiple test tones generated by BIST circuit [13].

The BIST approach, however, requires a special circuitryand its overhead becomes larger as the device size scales

down at mmWave frequency. The BIST circuitry generallyforms a wire connection to the system under test whichresults in antenna mismatch that is not presented in the cali-bration process. The compatibility across package is anotherrestriction to be considered in implementing BIST circuits.To address these issues, several researchers propose over-the-air (OTA) calibration of the phase and gain of phasedarray [15]–[19]. Some of these methods use amplitude-onlymeasurement to estimate phase of each array element [16]–[18], while others use the mutual coupling of the array [15] orthe scattering parameters of the probe antenna and the phasedarray to compute the excitations of the antenna elements [19].Unfortunately, all these methods require a separate calibrationprocess prior to using the phased array for communication andhence, cannot correct for errors that are triggered by transistoraging, electrical stress or temperature changes.

This paper presents a new online phased array calibrationtechnique that enables calibrating the phased array duringthe communication process. This allows us to continuouslycalibrate the phased array without the need for expensiveequipment, specialized circuitry or a separate calibration pro-cesses that can only be done prior to using the phased arrayfor communication. The key idea is to leverage the wirelesschannel estimation protocol that is an inherent part of anywireless communication system. By changing the phase shiftervalues and monitoring how the phase and magnitude of thewireless channel changes in response, we can calibrate thephased array to maximize the received power and minimizethe beam’s sidelobes. Specifically, by performing the channelestimation while changing the phase of an antenna element, thephase response of the element can be estimated. The relativephase of the phased array can then be obtained by collectingall the estimated phase responses with a shared referencestate which allows us to resolve the phase mismatches of thephased array. Our calibration method embraces all the arraycomponents such as power-divider, phase shifter, amplifier andantenna. Thus, the proposed method spans the full chain unlikeprior work which is limited to a few selected components.

Since calibration takes place during the communicationprocess, no additional measurements are required and in-fieldcalibration is possible to adapt to system conditions such astemperature. We have implemented and tested our techniqueon a 24 GHz phased array with 8 antenna elements whichwe had designed and fabricated in PCB for verifications. Ourresults show that we can reduce the sidelobe leakage for thearray by up to 7.3dB and our measured beam patterns provethe viability of our method.

II. PRIMARY

A. Phased Array

A phased array system is composed of an array of antennaelements that is spaced with a distance d as shown in Fig. 2.Each antenna element is connected to a phase shifter that iscapable of changing the phase of the input signal. If a signalis arrived at a certain angle, θ, the distance traveled by thesignal at the antenna element will be different by d cos θ with

Fig. 2. Phased Array System. Phased array system can steer a beam at adirection θ by shifting the phase of signals.

its neighbor element. Mathematically, the power P of signalsarriving along the direction θ can be written as:

P (θ) =

Np∑n=1

ej2πnd cos θ+φn

λ (1)

where φn is the phase change by the n-th phase shifter and λis the wavelength of the signal. By setting the phase shift φnequal to −nd cos θ, the power is maximized at the directionθ, and thereby the beam is steered to the desired direction.

B. Channel Estimation

In wireless communication, the received signal is corruptedby the channel response such as attenuation, phase shift, andnoise. Therefore, estimating and correcting the channel is oneof the key processes to recover the symbols at the receiver.Even our proposed method works with any wireless com-munication schemes, we use Orthogonal Frequency-DivisionMultiplexing (OFDM) not only because it is one of prominentcommunication scheme in WiFi and LTE but also because itschannel estimation is simple and efficient to be implemented.

Wireless signals transmitted over the air suffer inter-symbol interference (ISI) due to multipath channel effectand frequency-selective fading. In conventional single-carriersystem, complicated equalization techniques are adopted tosolve the issues. To combat these problem, multi-carrier mod-ulation scheme is developed. OFDM divides a spectrum bandinto many small and partially overlapping subcarriers, andmodulates the symbols on the subcarriers. The subcarriers arechosen to be orthogonal so that the inter-carrier interferencesums up zero. The OFDM output signal at the transmitter isgiven by

x(t) =

N−1∑k=0

X(fk)ej2πfkt

N (2)

where fk is the k-th subcarrier frequency. The above equationis an N-point inverse discrete Fourier transform (IDFT), whichcan be implemented in Fast Fourier transform requiring onlyO(N logN) computation. Once the transmitter performs theIFFT to convert the symbols in the frequency domain to Ntime domain samples, the receiver converts the signal back tothe frequency domain using the FFT, where each subcarrier isdemodulated independently.

Let Xi,k is the transmitted OFDM symbol at the time indexi and the frequency index k. The received OFDM symbol Ri,kcan be written as

Ri,k = HkXi,k + w (3)

where Hk is the frequency response of the channel at k-thfrequency index and w is the additive Gaussian white noise(AWGN). If a pilot OFDM symbol at i = −1 is sent beforethe data OFDM symbols (i = 0, 1, 2, ...), Hk can be estimatedby the Least Squares (LS) method as:

Hk =R−1,k

X−1,k(4)

Therefore, the channel estimation in OFDM can be performedin much simpler way than the conventional communicationscheme.

III. PROPOSED METHOD

A. Channel Model for Phased Array

Consider the channel including Np number of phase shifters.The received OFDM symbols can be written as

Ri,k = HkXi,k (5)

=(a0e

jφ0 +

Np∑n=1

anejφn)Xi,k (6)

where an and φn are the magnitude and phase response ofn-th antenna element, respectively. The leakage of the phasedarray is represented by a0e

jφ0 . To see how a phase shiftercontributes to the channel, the channel constellation measuredat the receiver is shown in Fig. 3 (a). As described in Equation6, the total channel is the sum of the complex numbers whosevalues are determined by the response of the phase shiftersand the leakage. If one of the array element changes its phasefrom 0 to 2π, the channel constellation will rotate a fullcircle. Therefore, the trajectory of the channel constellationcan indicate the response of an element.

As described in the previous section, the channel can beestimated by sending a pilot symbol at the time index i = −1.The frequency response of the channel from H0 to HN−1 ata given time can be obtained simultaneously. Therefore, themeasurement on wideband frequency response comes with freeby adopting OFDM scheme.

B. Formalizing the Problem

In practice, the magnitude and phase response of antennaelement has more complicated form than described in Equation6. If we look closely into one element, the response of oneelement can be written as a function of the control state, s:

fn(s) = an(s)ejφn(s)+ϕn (7)

where ϕn is a constant phase mismatch.There are two problems. First, the functions an(s) and

φn(s) are not identical over different element n. Therefore, themagnitude and phase are unknown at a given state. Second,even they are assumed to be identical over different element,

Fig. 3. Channel Estimation Constellation. (a) Each phase shifter contributesto the overall channel response. (b) The response of phase shifter is determinedby a given model. Changing the control state of the phase shifter will movethe channel response.

the phase mismatch term, ϕn, is unknown in general. Thephase mismatch is often dependent on the other componentssuch as power divider and antenna which are independent withthe state.

In this paper, we assume the response of the phase shiftersare not randomly different but share a similar characteristic.In section III-C, the shared model will assist to enhance theestimation. Consequently, the phase mismatch can be resolvedin section III-D.

C. Model-assisted Phase Estimation

We assume the phase shifters shares a common magnitudeand phase response that is known in priori. However, dueto manufacturing variation and mismatch, their output mea-surements are not identical. For example, two phase shifterscan share a common response but can create two differentchannel constellations. The actual constellation of the phaseshifters can be different due to 1) different magnitude andphase response to control state, 2) relative phase offset, and3) noise. In practice, the magnitude response is not flat overthe phase shifts. Thus, the constellation does not necessarilyform a circle while the phase is shifting from 0 to 2π, whichmakes the estimation difficult.

Suppose (in, qn) is the unknown center of thetrajectory on the constellation of the n-th elementand (in(1), qn(1)), (in(2), qn(2)), ..., (in(Ns), qn(Ns))are the measurements at Ns discrete phase states. Theobjective is to find the best estimate of the center giventhe measurements and the model response. Considerthe vectors vn(1) = [in(1), qn(1)]T − [in, qn]T andvn(2) = [in(2), qn(2)]T − [in, qn]T as shown in Fig. 3 (b).

vn(2) can be obtained by rotating θ2 and scaling c2 onvn(1). It can be described as

S(c2)R(θ2)vn(1) = vn(2) (8)

S(c2)R(θ2)

[in(1)− inqn(1)− qn

]=

[in(2)− inqn(2)− qn

](9)[

in(2)qn(2)

]− S(c2)R(θ2)

[in(1)qn(1)

]=(I− S(c2)R(θ2)

)[inqn

](10)

By defining

ym =

[in(m)qn(m)

]− S(cm)R(θm)

[in(1)qN (1)

](11)

am = I− S(cm)R(θm) (12)

, Equation 10 can be written as:

y2 = a2x (13)

where xn is the unknown center[inqn

], S(c) is the scaling ma-

trix[c 00 c

]and R(θ) is the rotation matrix

[cos θ − sin θsin θ cos θ

].

Note that matrix S and R are determined by the model. 2-by-2 system matrix in Equation 13 can be expanded to 2(Ns −1)-by-2 system by observing all Ns constellation points asfollows:

y2

y3

...yNs

=

a2a3...

aNs

xn (14)

Y = Axn (15)

The above system is linearly over-determined, 2(Ns − 1)observations for two unknowns. It is a linear regressionproblem that estimates the unknown model parameter, xn,from the data. Linear least square estimation minimized thesum of squared residuals:

xn = (ATA)−1ATY (16)

where xn =

[inqn

]is the least squared estimation for the center.

D. Phase Mismatch Calibration

Once we estimated the center of the n-th element, themagnitude and phase of state m can be calculated as:

an(m) = |vn(m)| (17)φn(m) = ∠vn(m) (18)

where vn(m) =

[in(m)qn(m)

]− x.

The relative phase mismatch between the antenna elementscan be calculated by comparing the phase at a reference state.For example, we set the first element as the reference elementand the first state as the reference state. The relative phase

between the reference element and the n-th element is equalto the difference of the phase at the reference states.

∆φn = φn(1)− φ1(1) (19)

It is a reasonable assumption that the phase offset is indepen-dent with the control state and has a fixed constant value foreach element because the sources of the mismatch are oftenpassive components such as power divider and patch antenna.

E. Handling Synchronization Offsets

In order to achieve a correct channel estimation on wirelesschannel, the transmitter and receiver are required to be syn-chronized by estimating and canceling the carrier frequencyoffset (CFO) and sampling frequency offset (SFO). The esti-mation of the CFO/SFO will be affected while changing thephase of the antenna. This issue can be resolved by addinga single static antenna on each Tx and Rx to form a staticchannel. The CFO/SFO estimation on the static channel canbe used to cancel the frequency offset between Tx/Rx, and thusthe synchronization can be achieved during the phase changes.

IV. HARDWARE IMPLEMENTATION

We designed and built a mmWave phased array system toevaluate the proposed method. The hardware block diagramshown in Fig. 4 (a) is implemented by the commercialoff-the-shelf components. NI USRP-2920 is used for an IFand baseband signal processing unit and transmites/receivesOFDM baseband signals. We use HMC815 and HMC977 eval-uation board for 24GHz I/Q up-converter and down-converter,respectively. The up/down-converts include an internal poweramplifier/LNA, an IQ mixer, and a frequency doubler. Weuse LMX2594 PLL evaluation board to generate the LOsignal at 11GHz for the IQ up/down-converters. A prototypephased array test board was fabricated on printed circuitboard (PCB) on Rodgers substrate as shown in Fig. 4 (b).The power splitter and the patch antenna were simulated anddesigned by Advanced Design System. The phased array boardincludes 8 antenna elements spaced by λ/2. The RF inputsignal is splitted by the transmission line and fed into 24GHzanalog phase shifters (HMC-933). The control voltage for thephased shifter is generated by a 8-bit DAC (AD7228A). TheDAC is controlled by Arduino Duo micro-controller whichis synchronized with USRP through the PC. For calibrationand measurement, the phased array is used for the transmitterantenna. We use a K-band horn antenna from SAGE for thereceiver antenna. The horn antenna has 22dBi gain and 12degree 3dB beamwidth.

V. EXPERIMENTAL RESULTS

The proposed calibration method is evaluated on 8-element24GHz phased array. To calibrate the phased array on thetransmitter, we use the horn antenna at the receiver side facingtoward transmitter. The control voltage is swept from 0V to10V while the transmitter and the receiver are communicatingOFDM packets. Fig. 5 shows the measured channel constel-lation at two different elements. We import the magnitude

USRPIQ

Upcvt

PLL

USRPIQ

Downcvt

PLL

DAC

RF:24GHz

RF:24GHz

LO:11GHz

LO:11GHz

IF:2GHz

IF:2GHz

Controlvoltage

PhasedArrayHornantenna

Transmitter Receiver

24GHzPhaseshifters

(a) (b)

Fig. 4. Hardware Block Diagram and Phased Array. (a) Block diagram of the mmWave transmitter and receiver system we built. (b) The 8-elementphased array. Each 24GHz phase shifter is connected to a patch antenna. The control voltage is provided by an external DAC through the connector.

Fig. 5. Measured Channel Estimation and Model. The figure shows thechannel estimation from two phase shifters with the fitted model. The relativephase can be evaluated by comparing the reference state.

Fig. 6. Estimated Gain and Phase. The figure shows the estimated gain andphase of the 8 phase shifters over the control voltage. The red dots shows thespecification of the phase shifter.

and phase specification of the phase shifters (HMC-933) andestimate the center for the trajectory. We run the calibration10 times for each 8 element. The gain and phase estimated forthe 8 elements by the channel estimation is plotted in Fig. 6.The red circles represents the specification of the phase shifter.The figure shows that a few phase shifters have a huge phaseoffset more than 100 degree. This phase mismatch will degrade

Control Voltage (V) Control Voltage (V)

Phas

e Sh

ift (d

egre

es)

Gai

n (d

B)

Standard Deviation

Fig. 7. Stability of Calibration. Standard deviation of calibration result.The figure shows that the calibration is stable within 1dB gain deviation and5 degree phase deviation.

CDF

Sidelobe Level (dB)

Fig. 8. Performance of Calibration. CDF of sidelobe level relative to themain beam with and without calibration. The figure shows that calibrationsignificantly reduces the radiation outside of the main beam.

the beam pattern without a proper calibration. In Fig. 7, thestandard deviation of the gain and phase calibration result isshown. The result shows the calibration is stable enough thatthe standard deviation of the gain and phase are less than 1dBand 5 degree, respectively.

To evaluate the beam pattern with calibration, the phasedarray is mounted on a pole equipped with a precise step motor.We setup the phase shifters of the array to steer at a specificangle, then we rotate the phased array antenna from 0-180degrees while the horn antenna is receiving the transmittedsignal. We measure the received power at each angle whichgives us the radiation pattern. In Fig. 9, we set the phasedarray to steer the beam at 9 different angles (50-130 degree, 10degree step) and compare the beam patterns with and withoutcalibration. For the sake of clarification, the peak magnitude is

50∘ 60∘

70∘ 80∘

90∘ 100∘

110∘ 120∘

130∘

Fig. 9. Beam Patterns. The measured beam patterns steered at 9 differentangles are shown. The beam patterns before (black) and after (red) calibrationare compared. The peak magnitude is normalized for better visualization.

normalized in both cases. In general, the peak power withoutthe calibration is smaller than with the calibration becausethe signal power is not focused at one direction. The beampattern with calibration shows that the main lobe is narrowerand the side lobe levels are lower than without calibration.For each measured beam pattern, we calculate the side lobelevel (SLL) which is the side lobe power relative the mainlobe. Higher SLL means that the antenna leaks more poweroutside the main lobe. Fig. 8 compares the CDF of SLL withand without calibration. The 90th percentile of SLL is -1.3dBwithout calibration, while it reduces to -8.6dB with calibration.The result implies that calibration reduces side lobe power andimproves the directionality of the phased array.

We observed that the beam patterns with calibration stillhave higher side lobes than the theoretical value. The mainreason for this is because of the magnitude mismatch betweenthe elements. We do not calibrate the magnitude mismatch inthis work because our hardware does not support the controlover the magnitude for each element. This problem will befurther studied in the future work.

VI. CONCLUSION

In this paper, we present a new online OTA calibrationmethod for mmWave phased array. Due to the small wave-length, mmWave phased array is very sensitive to small offsets,which makes calibration difficult. Our method exploits channelestimation in wireless communication in order to measure themagnitude and phase response of the phased array system.Therefore, our calibration can be online not necessarily topause the communication and does not need extra circuits.

We implemented an 8-element 24GHz phased array systemto evaluate our calibration. The hardware measurement resultsprove that our calibration is capable of compensating the phasemismatches and improves the beam pattern by reducing SLL.

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